Bolt Circle Calculator

How Bolt Circle Calculations Work

A bolt circle (also called a bolt pattern or pitch circle) is a circular arrangement of equally spaced holes used in flanges, couplings, wheels, and machinery. Given the pitch circle diameter (PCD) and the number of bolts N, the key values are:

• Radius (R): R = PCD / 2
• Angular spacing: 360 / N degrees between each hole
• Chord length: the straight-line distance between adjacent bolt centres = PCD × sin(π / N)
• XY coordinates of bolt i (0-indexed): x = cx + R × cos(start + i × 360/N), y = cy + R × sin(start + i × 360/N)

Angles are measured in degrees from the positive X axis (3 o'clock direction), increasing anticlockwise. You can shift the start angle to place the first bolt at any position, for example 90 degrees to put the first bolt at the top (12 o'clock).

Worked Example

Defaults: 6 bolts on a 100 mm PCD, start angle 0 degrees, origin at (0, 0).

• Radius = 100 / 2 = 50.00 mm
• Angular spacing = 360 / 6 = 60.00 degrees
• Chord length = 100 × sin(180 / 6) = 100 × sin(30°) = 100 × 0.5 = 50.00 mm
• Bolt 1 (0°): X = 50.00, Y = 0.00
• Bolt 2 (60°): X = 25.00, Y = 43.30
• Bolt 3 (120°): X = -25.00, Y = 43.30
• Bolt 4 (180°): X = -50.00, Y = 0.00
• Bolt 5 (240°): X = -25.00, Y = -43.30
• Bolt 6 (300°): X = 25.00, Y = -43.30

Common Bolt Patterns

How to Measure PCD on an Existing Part

If you need to find the PCD of an existing bolt pattern, measure the distance between the centres of two adjacent bolt holes using a vernier calliper. Then use the formula: PCD = chord / sin(π / N). For example, if you measure 50 mm between adjacent holes on a 6-bolt pattern: PCD = 50 / sin(30°) = 50 / 0.5 = 100 mm. For a 4-bolt pattern, measure the centre-to-centre distance of two diagonally opposite bolts; that distance is equal to the PCD.

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Method: Standard bolt circle trigonometry. Coordinates: x = cx + (PCD/2) × cos(θ), y = cy + (PCD/2) × sin(θ) where θ = start_angle + i × (360/N) in degrees. Chord length = PCD × sin(π/N). All values computed in double-precision floating point.

This calculator is for planning and reference purposes. Always verify dimensions with calibrated measuring equipment before machining or fabrication. Coordinate precision is to 4 decimal places; round to your required tolerance for workshop use.